Stability Analysis of Torsional Vibrating Systems with Delayed Vibration Absorbers

It is universally acknowledged that using delayed vibration absorbers can effectively reduce vibrations in torsional vibrating systems. When the absorbers are adopted, choosing appropriate gains of absorbers and delays is extremely important. In this paper, the stability analysis of torsional vibrating systems with delayed vibration absorbers is studied. Based on the Lyapunov-Krasovskii method and integral inequality techniques, stability conditions for the torsional vibrating systems with the delayed vibration absorbers are obtained. According to the conditions, the relationship among the gains, the delays and the stability of the systems are shown. It means that the conditions can be used to adjust the gains and the delays effectively. At last, a case study is given to show the effectiveness of the obtained conditions.